GHCで {リスト,スカラ} x {リスト,スカラ}演算のオーバーロード

overload.hs

{-#LANGUAGE TypeFamilies, MultiParamTypeClasses, FlexibleInstances #-}

class Overload a b where
  type Out a b :: *
  (+):: a -> b -> Out a b

instance Overload Int Int where
  type Out Int Int = Int
  (+) = (Prelude.+)

instance Overload [Int] Int  where
  type Out [Int] Int = [Int]
  (+) a b = map (Prelude.+ b) a

instance Overload  Int [Int]  where
  type Out Int [Int] = [Int]
  (+) a b = map (a Prelude.+) b

instance Overload  [Int] [Int]  where
  type Out [Int] [Int] = [Int]
  (+) a b = map (uncurry (Prelude.+)) $ zip a b



main :: IO ()
main = return ()